TITLE: How does all of the bundles over a certain manifold characterize the homotopy class of the base manifold?
QUESTION [8 upvotes]: It is known that if $f:M\rightarrow N$ is a homotopy equivalent, then the the process of pullback gives a one-one correspondence between bundles over $N$ and $M$ up to isomorphism. Is the converse( that if $f$ gives a 1-1 correspondence between them, then $f$ is a homotopy equivalence)true? Or any counterexample?
By the way, are bundles of a fixed rank over a compact manifold finite up to isomorphism? And is there any characterization of them like the holomorphic line bundles as a first cohomology group of a certain sheaf? If so, is there any way to calculate?

$M,N$ are smooth manifolds, and I originally thought of real vector bundles. But since this is a wild guess, it might be better to think the most general bundles you could imagine that homotopy invariance holds, even though I only know the real case.
It seems algori's answer apply to all kind of vector bundles I can imagine, though a bit beyond me. Thanx very much. And any reference for your arguments? 
And I'd like to know whether homotopy invariance holds in fiber bundles.

Thanks all of you. But formally whose answer should I accept?

REPLY [2 votes]: All the above answers are great, but as you are just learning this stuff, the following might be helpful. Vector/$G$-bundles contain actual geometric information! The tangent bundle, for example, tells you a lot about the geometric structure of the underlying manifold (some definitions of curvature etc.). Now a homotopy theorist can measure these things using cohomology and homotopy as described above by Algori and Mark Grant. So cohomology restricts what kind of bundles you can have (are they trivial? how many linearly independent sections might they have?). Chern-Weil theory might be something to look up if this sounds cool.
Something to note though, all vector bundles are homotopy equivalences.
Also, Peter May wrote a little memoir called Classifying spaces and fibrations where he writes down classifying spaces for fibrations with fiber $F$. These have significantly less structure than a plain old fiber bundle. Granted, there are restrictions on when we have classification, but usually they are pretty harmless, and any compact smooth manifold should satisfy them.